Another vote here for EMI.
I've seen something similar on a project that I worked on recently - but this caused the processor to go off into space. The fix was easy, but it took a while to figure out what was going on.
+1
A small DC motor was causing noise on my 1-wire communication network. The PIC was reseting once in a while without reason. It stopped when I placed a
ferrite bead on the cable going from my control box to the motor. Took a while to find out what was going on too. That kind of non-replicable bug can be a pain.